Gamma decay of unbound neutron-hole states in 133Sn

V. Vaquero,1 A. Jungclaus,1, ∗ P. Doornenbal,2 K. Wimmer,3 A. Gargano,4 J.A. Tostevin,5 S. Chen,2, 6

E. Nacher,1 E. Sahin,7 Y. Shiga,8 D. Steppenbeck,2 R. Taniuchi,2, 3 Z.Y. Xu,9 T. Ando,3 H. Baba,2

F.L. Bello Garrote,7 S. Franchoo,10 K. Hadynska-Klek,7 A. Kusoglu,11, 12 J. Liu,9 T. Lokotko,9

S. Momiyama,3 T. Motobayashi,2 S. Nagamine,3 N. Nakatsuka,13 M. Niikura,3 R. Orlandi,14

T. Saito,3 H. Sakurai,2, 3 P.A. Soderstrom,2 G.M. Tveten,7 Zs. Vajta,15 and M. Yalcinkaya11

1Instituto de Estructura de la Materia, CSIC, E-28006 Madrid, Spain2RIKEN Nishina Center, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan

3Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan4Istituto Nazionale di Fisica Nucleare, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy

5Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom6School of Physics and State Key Laboratory of Nuclear Physics and Technology,

Peking University, Bejing 100871, People’s Republic of China7Department of Physics, University of Oslo, NO-0316 Oslo, Norway

8Department of Physics, Rikkyo University, Tokyo, Japan9Department of Physics, The University of Hong Kong, Pokfulam, Hong Kong

10Institut de Physique Nucleaire Orsay, IN2P3-CNRS, 91406 Orsay Cedex, France11Department of Physics, Faculty of Science, Istanbul University, Vezneciler/Fatih, 34134, Istanbul, Turkey12ELI-NP, Horia Hulubei National Institute of Physics and Nuclear Engineering, 077125 Magurele, Romania

13Department of Physics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan14Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan

15MTA Atomki, P.O. Box 51, Debrecen H-4001, Hungary(Dated: April 5, 2017)

Excited states in the nucleus 133Sn, with one neutron outside the doubly-magic 132Sn core, werepopulated following one-neutron knockout from a 134Sn beam on a carbon target at relativisticenergies at the Radioactive Isotope Beam Factory at RIKEN. Besides the γ rays emitted in thedecay of the known neutron single-particle states in 133Sn additional γ strength in the energy range3.5-5.5 MeV was observed for the first time. Since the neutron-separation energy of 133Sn is low,Sn=2.402(4) MeV, this observation provides direct evidence for the radiative decay of neutron-unbound states in this nucleus. The ability of electromagnetic decay to compete successfully withneutron emission at energies as high as 3 MeV above threshold is attributed to a mismatch betweenthe wave functions of the initial and final states in the latter case. These findings suggest that in theregion south-east of 132Sn nuclear structure effects may play a significant role in the neutron vs. γcompetition in the decay of unbound states. As a consequence, the common neglect of such effectsin the evaluation of the neutron-emission probabilities in calculations of global β-decay propertiesfor astrophysical simulations may have to be reconsidered.

PACS numbers: 21.10.Ky, 21.60.Cs, 27.60.+j

The atomic nucleus offers a unique opportunity tostudy the competition between three of the four fun-damental forces known to exist in nature, namely thestrong nuclear interaction, the electromagnetic interac-tion and the weak nuclear interaction. Only the muchweaker gravitational force is irrelevant for the descriptionof nuclear properties. In general, the decay of an excitednuclear state follows the hierarchy of these forces. Theemission of one or more particles mediated by the stronginteraction dominates the decay of unbound states whilebound excited states usually decay by electromagneticradiation until the ground state is reached. Finally, thelatter decays via β decay mediated by the weak nuclearinteraction. The different strengths of these interactionsare reflected by the time scales of the above mentionedprocesses, ranging from typically 10−22 s for fast particledecays to 107 s for slow β decays and 1030 s for doubleβ decays. Of course there are exceptions to this general

rule. There are many cases known in which β decay winsagainst electromagnetic decay because the latter requiresthe emission of a γ ray of high multipolarity and/or lowenergy. In the case of the strong force the Coulomb bar-rier can defer the emission of charged particles and allowelectromagnetic decay to compete above the separationenergy. In the case of neutron emission on the neutron-rich side of the nuclear chart, in the absence of a Coulombbarrier, only the angular momentum barrier may hinderthe neutron emission and thus favour γ decay. Indeed γ-decaying high-spin states above the neutron-separationenergy have been identified in several neutron-rich nu-clei. In general, however, it is assumed that neutron de-cay dominates for all low- to moderate-spin states abovethe neutron threshold. This assumption is commonlyused in theoretical calculations of global β-decay proper-ties which are employed for astrophysical calculations, forexample for the description of the rapid neutron-capture

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process (r process) of nuclear synthesis.However, according to Fermi’s golden rule the proba-

bility of a certain decay process to occur does not onlydepend on the strength of the interaction and the den-sity of final states but also on the overlap between thewave functions of the parent and daughter states [1]. Bymeans of this latter ingredient nuclear structure effectscan influence decay rates and thus have an impact forexample on the competition between neutron emissionand γ deexcitation above the neutron-separation energyin neutron-rich nuclei. In recent years several cases havebeen reported in which electromagnetic decay success-fully competes with neutron emission in the decay of un-bound states with excitation energies up to more than 2MeV above the neutron-separation energy [2–5], i.e. wellbeyond the first few hundred keV where neutron emis-sion is hindered by the low penetrability. In some ofthese works nuclear structure arguments based on theo-retical calculations have been put forward to explain theexperimental findings. On the neutron-deficient side ofthe nuclear chart, the γ decay of isobaric analog statesfar above the proton-separation energy has been observedin fp shell nuclei and explained by the fact that protonemission is isospin forbidden in these cases [6, 7].

In this Letter we investigate the nuclear structure as-pect in the decay of unbound states by means of a verysimple nuclear system, namely the nucleus 133Sn. Thisnucleus has only one valence neutron in the N = 82-126 major shell outside 132Sn, which is generally consid-ered as a very robust doubly-magic core. Neutron single-particle energies (SPE) of 854, 1367, 1561, and 2002 keVfor the 2p3/2, 2p1/2, 0h9/2, and 1f5/2 orbitals, respec-tively, relative to the 1f7/2 orbital, have been establishedcombining the information from both β decay and (d,p)neutron-transfer experiments [8–11]. For the 0i13/2 SPEan energy range of 2360-2600 keV has recently been pro-posed based on the systematics of 13/2+ levels in N = 83nuclei in comparison with shell-model calculations [12].The neutron single-hole states in 133Sn are expected atexcitation energies far above Sn. In Ref. [8], a line at1.26 MeV in the neutron spectrum measured followingthe β decay of 134In has tentatively been assigned to thedecay of the 0h−1

11/2 hole state in 133Sn positioning this

state at an excitation energy of around 3.66 MeV (Sn= 2.402(4) MeV [13]). The present work reports on thestudy of the γ decay of excited states in 133Sn populatedvia one-neutron knockout from 134Sn at relativistic ener-gies.

The experiment was performed at the Radioactive Iso-tope Beam Factory operated by the RIKEN Nishina Cen-ter for Accelerator-Based Science and the Center for Nu-clear Study of the University of Tokyo. Secondary ra-dioactive beams were produced via projectile fission of a345 MeV/u 238U beam with an average intensity of 15pnA, impinging on a 4-mm thick Be target. The ions ofinterest were separated from other reaction products and

identified on an ion-by-ion basis by the BigRIPS in-flightseparator [14]. The particle identification was performedusing the ∆E-TOF-Bρ method in which the energy loss(∆E), time of flight (TOF) and magnetic rigidity (Bρ)are measured and used to determine the atomic num-ber, Z, and the mass-to-charge ratio, A/q, of the frag-ments. Details about the identification procedure can befound in Ref. [15]. The identified 134Sn ions then im-pinged with a kinetic energy of 165 MeV/u on a 3-mmthick C target. Reaction products created via nucleonremoval left the target with energies around 115 MeV/uand were identified in the ZeroDegree (ZD) spectrometer[14] employing again the ∆E-TOF-Bρ method. Total re-action cross sections for the removal of x neutrons, σxn,were determined from the yield of the respective reactionproducts detected in the ZD spectrometer and the num-ber of incoming projectile ions taking into account thetransmission through the ZD spectrometer, losses due toreactions with detector material along the beam line andthe properties of the C target. To detect γ radiation emit-ted from excited reaction residues the secondary targetwas surrounded by the DALI2 spectrometer [16]. DALI2consisted of 186 NaI(Tl) detectors, covering polar anglesin the range from 20 to 150 degrees, and had a photopeak efficiency of 15% for the 1.33-MeV γ ray emittedby the stationary 60Co source.

Fig. 1 shows the Doppler-corrected γ-ray spectrummeasured in coincidence with 134Sn ions detected inBigRIPS and 133Sn nuclei detected in the ZD spectrome-ter. The three lines at energies of 854, 1561, and 2002 keVcorrespond to the decays of the 2p3/2, 0h9/2, and 1f5/2

FIG. 1. (color online). Doppler-corrected γ-ray spectrum (forγ-ray multiplicity Mγ = 1 after add-back) of 133Sn populatedvia one-neutron knockout from 134Sn. The response functionfit to the experimental spectrum is shown by the thick red linewhile the individual components are shown as thin black lines.The background is indicated as grey area. The inset showsthe high-energy region of the spectrum on a linear scale.

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single-particle states to the 1f7/2 ground state while the513-keV γ ray depopulates the 2p1/2 state at 1367 keVto the 2p3/2 level at 854 keV [11]. Besides these known γrays clearly additional γ strength is observed above theneutron separation energy, reaching up to about 5.5 MeV.To describe the experimental spectrum the response ofthe DALI2 array to the incident γ radiation was simu-lated using GEANT4 [17]. In these simulations the pre-cise γ-ray energies determined in Ref. [11] were employed.To increase the detection efficiency for high-energy γ raysand to improve the peak-to-total ratio over the full energyrange an add-back algorithm was applied. All energy de-positions registered in NaI crystals within a range of 15cm from the center of the crystal with the highest en-ergy signal were summed. Doppler correction was thenperformed assuming that the largest energy depositioncorresponds to the first interaction of the γ ray in the ar-ray and using the mid-target velocity of β = 0.497. Thebackground in the spectrum shown in Fig. 1 has beenparametrized by the sum of two exponential functionscutoff at low energy with an error function. Up to theneutron separation energy the experimental spectrum iswell described by the sum of the background and theDALI2 response to the listed γ rays. For the 854-keVline, however, a small shift with respect to the nominalenergy was observed when only the most forward crys-tals of DALI2 were considered as shown in Fig. 2a). Thisshift points to a lifetime of a few tens of ps for the 854-keV state because in that case the γ ray emission takesplace at a lower average recoil velocity than assumed inthe simulation. On the basis of a comparison betweenthe experimental line shapes, obtained for two differentangular ranges of DALI2 detectors, and simulations as-suming different lifetimes a value of τ = 30(15) ps wasdeduced for the state at an excitation energy of 854 keV(see Fig. 2). From this lifetime a transition strength ofB(E2) = 1.6(8) W.u. is calculated for the 2p3/2→1f7/2E2 transition in 133Sn. This strength is comparable tothat of the 2d5/2→1g9/2 and 3s1/2→2d5/2 neutron single-particle transitions in 209Pb (B(E2) = 2.5(7) W.u. andB(E2) = 2.13(8) W.u., respectively [18]). Coming backto the spectrum shown in Fig. 1, the strongest peak aboveSn is well described by the DALI2 response to a singleγ ray with an energy of 3570(50) keV. With respect tothe γ strength at even higher energy, unfortunately thelimited statistics and poor energy resolution prohibit amore detailed analysis of its distribution.

To interpret the γ-ray spectrum of 133Sn the reactionprocess which led to the population of excited states inthis nucleus has to be considered. In principle the neu-tron removal can proceed from any neutron orbital whichis occupied in the ground state of the projectile nucleus,in this case 134Sn. Considering the single-particle en-ergies in 133Sn it is expected that the valence-neutronpair in 134Sn occupies dominantly the 1f7/2 orbital. Aknockout from this orbital results in the ground state of

FIG. 2. (color online). Comparison between the experimentalline shape of the 854-keV line observed in the DALI2 detectorsat polar angles a) <67◦ and b) >67◦ with respect to the beamaxis and simulations assuming lifetimes of τ = 0 ps (blue lines)and τ = 30 ps (red lines) for the 854-keV state.

133Sn and consequently no γ ray is emitted in this case.However, also the other neutron orbitals of the N = 82-126 shell contribute to the composition of the wave func-tion, i.e. there is a certain probability for the neutronpair to occupy the 2p3/2, 2p1/2, 0h9/2, 1f5/2, and 0i13/2orbitals. Shell-model calculations using realistic effec-tive interactions [19] predict an 80% probability for thevalence-neutron pair to occupy the 1f7/2 orbital and con-tributions between 1.6% and 5.2% for all other orbitalsof the N = 82-126 shell. One-neutron knockout from the2p3/2, 2p1/2, 0h9/2, and 1f5/2 orbitals will populate theknown bound single-particle states in 133Sn which decayvia γ-ray emission to the ground state. Consequently, the513-, 854-, 1561-, and 2002-keV transitions are all clearlyvisible in the spectrum shown in Fig. 1. With respect tothe yet unknown position of the 0i13/2 orbital we notethat in the present experiment no γ ray is observed inthe expected energy range (Ex = 2360-2600 keV [12]).

Besides the removal of one of the two valence neutronsalso the knockout of a neutron from the closed N = 82core can occur. In this case neutron-hole states in 133Snare populated as illustrated in Fig. 3a). Although knock-out can proceed from all five orbitals of the N = 50-82shell, the largest cross section is expected for the 0h11/2orbital since it is close to the Fermi level and occupied byas many as twelve neutrons. We therefore suggest thatthe 3570(50)-keV transition corresponds to the decay ofa 11/2− state to the ground state. Note that this en-ergy is close to the 3.66 MeV proposed by Hoff et al. onthe basis of neutron spectroscopy [8]. Since this excitedstate lies above the neutron-separation energy, it can de-cay either via neutron emission or electromagnetic decay,see Fig. 4. As already discussed in the introduction, ex-cited states above Sn are generally expected to decayvia neutron emission rather than γ deexcitation. Dueto the high excitation energy of the first excited state in132Sn, Ex(2+) = 4.041 MeV, the presumed 11/2− stateat 3570(50) keV can only neutron decay to the groundstate of 132Sn, i.e. via the emission of an `=5 neutron

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-1 0 1 2 3 4 5 6 7 8 9 10E (MeV)

-15

-10

-5

() 0g7/2

1d5/2

2s1/2

0h11/2

1d3/2

1f7/2

2p3/2

2p1/2

0h9/2

1f5/2

0i13/2

82

-1 0 1 2 3 4 5 6 7 8 9 10E (MeV)

-15

-10

-5

()

82

neutron knockout from 0h11/2

133Sn

n γ

-1 0 1 2 3 4 5 6 7 8 9 10E (MeV)

-15

-10

-5

()

82

133Sn 132Sn

followed by γ decay followed by n emission

a) b) c)

FIG. 3. (color online). Schematic of the neutron orbital oc-cupancies a) after the knockout of a 0h11/2 neutron from the134Sn projectile, followed by b) γ decay or c) neutron emis-sion. Note that the energy distance between the 2s1/2, 0h11/2,and 1d3/2 orbitals is not to scale to allow for a better legibilityof the figure.

with a kinetic energy of about 1.2 MeV (En = Ex-Sn).The expected lifetime for this decay amounts to less than10−17 s. To estimate the lifetime for an E2 γ decay tothe 7/2− ground state, we assume a transition strengthof 2 W.u. in line with the experimental strength of sev-eral single-particle E2 transitions in 133Sn and 209Pb asdiscussed above. This estimate yields a lifetime of about10−14 s. Therefore, at the level of pure single-particletransitions, the neutron decay is expected to be roughlythree orders of magnitude faster as compared to γ-rayemission.

As mentioned above, an additional factor, which canaffect the competition between neutron and γ-ray emis-sion, is the overlap of the wave functions of the initialand final states. After the knockout of a core neutron,e.g. a 0h11/2 neutron, from the projectile 134Sn, 133Snis populated with a neutron configuration as shown inFig. 3a). In the case of γ decay, the hole in the N =50-82 core is filled by one of the two neutrons occupyingprimarily the 1f7/2 orbital in the ground state of 134Snand a 3570-keV γ ray is emitted. The final state corre-sponds to the ground state of 133Sn [see Fig. 3b)]. Neu-tron emission, on the other hand, yields a 132Sn nucleuswith two holes in the 0h11/2 orbital and two neutronsabove the N = 82 gap, i.e. in a two-particle-two-hole(2p-2h) state [see Fig. 3c)]. The ground state of 132Sn,however, is not expected to contain large contributionsof 2p-2h configurations and consequently the overlap ofthe wave function of the parent state with that of thedaughter state plus a neutron is small. It is this wavefunction mismatch which hinders neutron emission andallows electromagnetic decay to compete in the decay ofhighly-excited neutron-hole states in 133Sn. Note thatthe above reasoning is valid for all hole states in the N= 50-82 shell, not only the 0h11/2 hole.

In order to quantify the average γ-ray branching forstates above the neutron-separation energy in 133Sn, we

will discuss in the following the total cross sections forone-neutron knockout from 133Sn and 134Sn projectiles,σ1n, which are shown together with the cross sectionsfor multi-neutron removal, σxn, in Fig. 5. The measuredcross sections, σ1n = 183(21) mb for 133Sn and σ1n =69(10) mb for 134Sn, comprise contributions from boththe removal of a neutron from the valence space (N >82), σval1n , as well as knockout from the N = 50-82 core,σcore1n , as discussed above. These contributions were cal-culated using eikonal reaction theory [20, 21] and em-ploying the ground state wave functions from the shellmodel, the known SPE in 133Sn and excitation energiesfor the neutron-hole states from a spherical Hartree-Fock(HF) calculation. These calculations yield values of σval1n

∼14/20 mb and σcore1n ∼186/152 mb for knockout from133Sn/134Sn. For removal from 133Sn it is expected thatdue to the high neutron-separation energy in the daugh-ter nucleus 132Sn, Sn = 7.343(7) MeV [13], most of thehighly-excited states populated following the removal ofa neutron from the N = 50-82 core are bound and de-cay via γ-ray emission as illustrated in Fig. 4. Indeedthe calculated value, σ1n = σval1n + σcore1n ∼200 mb, isin good agreement with the measured cross section. Inthe case of knockout from 134Sn, in contrast, the resid-ual nucleus, 133Sn, has a low neutron-separation energyof only Sn = 2.402(4) MeV [13] and as a consequenceneutron removal from the core populates unbound stateswhich can decay either via neutron or γ-ray emission (seeFig. 4). In the case of neutron emission the final nu-cleus is identified as 132Sn in the ZD spectrometer andthe corresponding cross section is therefore assigned tothe two-neutron removal reaction. As a consequence the

0

5

10

15

20

Ener

gy (M

eV)

134Sn

133Sn

132Sn2.402

9.745 7.343

3.570

4.041

0

0

0

Sn

S2n Sn

0+

0+

2+

7/2- KO

N≤82

KO N≤82

KO N>82

KO N>82

n γ

(11/2-)

FIG. 4. (color online). Illustration of the population of bound(grey regions) and unbound (blue region) excited states in132,133Sn following one-neutron knockout (KO) from eitherthe valence space (N > 82) or the N = 50-82 core (N ≤ 82).In the case of 133Sn the positions of the known single-particlestates are indicated by thin black lines while in the case of132Sn these show the positions of the neutron-hole states asobtained from HF calculations. Energies are quoted in MeV.

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measured value of σ2n is larger as compared to σ1n (seeFig. 5). The cross section corresponding to γ-decayingunbound states in 133Sn can be estimated by subtractingthe calculated cross section for neutron removal from thevalence space to bound final states in 133Sn, amountingto σval1n ∼20 mb, from the measured σ1n = 69(10) mb.The resulting value of ∼49 mb, compared to the calcu-lated value of σcore1n ∼152 mb for knockout from the core,suggests that 25-35% of the decay of unbound states in133Sn, populated in the one-neutron knockout reaction,proceeds via γ-ray emission. Although this estimate issubject to several uncertainties it clearly shows that thecontribution of γ decay is significant.

The significant effect of nuclear structure on thecompetition between neutron and γ decay of unboundstates, demonstrated here by means of the simple nucleus133Sn, may have more general and further-reaching con-sequences. The β-decay properties of nuclei in the regionsouth-east of 132Sn are of great importance for the de-scription of the r process of nuclear synthesis [22, 23]. Inthis region, the β-decay energies, Qβ , are large and theneutron-separation energies, Sn, low, so that unboundexcited states in a wide energy window of more than 10MeV can be populated in the β decays. Experimentalinformation is scarce so that in many cases theoreticalcalculations of global β-decay properties have to be reliedupon. In the latter β-delayed neutron emission probabili-ties are deduced from calculated strength functions underthe assumption that neutron emission occurs wheneverit is energetically possible (see for example Eq. (21) ofRef. [24]). It is well known that for nuclei with Z < 50and N ≈ 82, the β decay is dominated by the ν0g7/2 →π0g9/2 Gamow-Teller transition [24, 25]. Also the first-

1 2 3 4 5 6number of removed neutrons x

0

50

100

150

200

xn (m

b)

FIG. 5. Total experimental cross sections for the removal ofx neutrons, σxn, from 133Sn (open squares) and 134Sn (filledcircles) projectiles. Lines are drawn to guide the eye. Thevertical bars for x=1 indicate the cross sections for knockoutfrom the N > 82 valence space (black) and from the N = 50-82 core (grey) as calculated using eikonal reaction theory. Thecontribution from the 0h11/2 orbital to the latter amounts to67 and 56 mb, respectively.

forbidden ν0h11/2 → π0g9/2 decay is known to play asignificant role. Beyond N = 82, once the 1f7/2 neutronorbital starts being occupied, both these transitions pop-ulate core-excited states at high excitation energy in thedaughter nuclei. In 132Sn and 131In, populated in the βdecays of the N = 83 isotones 132In [26] and 131Cd [27],excited states comprising a neutron hole in the 0h11/2(0g7/2) orbital have been identified in the energy rangeof 4-5 MeV (6-7 MeV). For the decay of these states, thesame structure arguments apply which have been putforward above in the discussion of the decay of highly-excited neutron-hole states in 133Sn. It therefore seemsadvisable to fully elucidate the neutron vs. γ-ray compe-tition in the decay of unbound excited states in exotic nu-clei south-east of 132Sn in future experiments, employingcomplementary techniques such as delayed-neutron spec-troscopy and total absorption gamma-ray spectroscopy.

To conclude we presented clear evidence for the electro-magnetic decay of states in 133Sn at excitation energiesup to more than 3 MeV above the neutron-separationenergy. These excited states are interpreted as neutron-hole states which are populated following the knockoutof a neutron from the closed N = 50-82 shell of the 134Snprojectile ion at relativistic energies. The ability of γ-rayemission to compete with neutron decay, despite a hin-drance of three orders of magnitude at the single-particlelevel, is explained taking into account the structure of theinitial and final states and the resultant wave-functionoverlap. Our study raises the question whether, due tonuclear structure effects, the γ-ray emission may play amuch more significant role than generally assumed in thedecay of highly excited states populated following β de-cay in the region south-east of 132Sn.

A.J. acknowledges fruitful discussions with H. Grawe,S.L. Tabor and J.L. Tain. We thank the staff of theRIKEN Nishina Center accelerator complex for provid-ing stable beams with high intensities to the experiment.This work was supported by the Spanish Ministerio deCiencia e Innovacion under contract FPA2011-29854-C04and the Spanish Ministerio de Economıa y Competitivi-dad under contract FPA2014-57196-C5-4-P. J.A.T. ac-knowledges the support of the Science and TechnologyFacilities Council (UK) grant ST/L005743 and R.O. thatof JSPS KAKENHI Grant No. 26887048. G.M.T. grate-fully acknowledges funding of this research from the Re-search Council of Norway, Project Grant No. 222287.

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